Representation Of Continuous Sup-Semilattices By Generalized Formal Concept Analysis

Domain theory was founded by Turing Award winner D.S.Scott.Its purpose is to provide a mathematical model for denotational semantics of functional programming languages.The main research objects of Domain theory are some special posets,which are usually called domain structures.The interaction between order and topology is the most remarkable feature of Domain theory.On the other hand,formal concept analysis(for short,FCA)was proposed by R.Wille whose original purpose was to establish a solid mathematical foundation for the application of lattice theory in data mining and knowledge representation,and has become an important research object in the field of artificial intelligence.In recent years,many scholars have been attempting to establish the relationship between Domain theory and FCA.Among them,Guo-Qiang Zhang proposed the notion of approximation concept which realizes a representation of algebraic lattices.This work inspires us to use FCA to study the representation of more domain structures.Our aim is to obtain the representation of continuous sup-semilattices by generalizing the classical FCA.The thesis is constructed as follows: In Chapter 1,we recall some basic concepts and related properties,and present the historical background.In Chapter 2,we firstly give the concept of continuous F-augmented formal context and study the relation between continuous F-augmented formal contexts and continuous sup-semilattices.Secondly,we give the concept of F-approximating map and show the relation between F-approximating maps and Scott continuous maps.Finally,we prove that continuous F-augmented formal contexts and F-approximating maps do form a category,and moreover,the category of F-augmented formal contexts is equivalent to the category of continuous sup-semilattices.